Senior Trump aide Kellyanne Conway has said her defence of “alternative facts” was a mistake that she has not been allowed to “brush off”.

In an interview scheduled to be broadcast on CBS Sunday Morning, the senior White House adviser compared her remark, which she said was a conflation of “alternative information and additional facts”, to the error last weekend that saw the Oscar for best picture given to La La Land instead of Moonlight.

Her experience under fire from the media, she said, had taught her women must have “bile in your throat” if they are to run for office or be involved in national politics.

Conway has been at the centre of several successive news storms since Donald Trump’s inauguration on 20 January. First, she said in a TV interview that when Trump press secretary Sean Spicer repeated falsehoods about inauguration crowds and protests across the country, he was presenting “alternative facts”.

Then Conway gave an on-camera recommendation of products sold by the president’s daughter, Ivanka Trump, which the Office of Government Ethics said breached rules and which led to a White House rebuke.

Asked by interviewer Norah O’Donnell about the now infamous “alternative facts” episode, which many critics seized upon to illustrate the Trump White House’s facility with dishonest or misleading statements , Conway said she had simply spoken in error.

“Well,” she said, “it was alternative information and additional facts. And that got conflated. But, you know, respectfully, Norah, I see mistakes on TV every single day and people just brush them off. Everybody thinks it’s just so funny that the wrong … movie was, you know, heralded as the winner of the Oscars.”

Asked whether she would consider a run for office herself, she said: “It’s not just the fire in your belly anymore. You have to have the bile in your throat. And this is why I think many women do not run for office. Many good men and women who would.”

O’Donnell interjected: “Bile in your throat?”

“Yeah,” Conway said, “just to swallow so much, that the country looks at you through this negative lens, you know corruption and cronyism and ‘You’re lying’ and ‘You want money and you’re motivated by power.’”

CBS also said the interview, which was filmed at Conway’s home in New Jersey, included comments from George Conway, her husband, who has been touted as a pick for solicitor general.

Conway also discussed the “triple standard” she was held to as a conservative woman, CBS said.

In an appearance last week at the CPAC conservative conference in Maryland, Conway said in remarks critical of the Women’s March and other protest movements it was “difficult to call myself a feminist in the classic sense, because it seems to be very anti-male and it certainly is very pro-abortion in this context and I’m neither”.

She added: “One thing that’s been a little bit disappointing and revealing and that I hope will get better is it turns out that a lot of women just have a problem with women in power.”

A political pollster by profession, Conway joined Donald Trump’s campaign for the presidency in August, as his third person to oversee his campaign after the departures of Corey Lewandowski and Paul Manafort. She previously worked for the Texas senator Ted Cruz, the runner-up in the Republican primary.

Conway was widely credited with imposing a measure of discipline on the erratic campaign, leading some observers to christen her as “the Trump whisperer”. She was also credited with finessing Trump’s message to white suburban women and for demonstrating an ability to navigate political interviews.

If anything would make her leave the White House, Conway told CBS, it would be her four children.

“They’re having the hardest time with this,” she said. “They’re great kids, but they’re really the worst ages for a mom to be … away from them, 12, 12, eight and seven. And 24/7 secret service protection is tough for them. It’s tough for them to think about when I’m away from them and why does she have that.

“This is all new for us,” she added. “This is not something I sought. I’m not a famous person on TV.”

Conway said her children were “ struggling because it’s just different to not have a mom there as much as they’re used to even though I’ve always worked. This is an entirely different level.”

Conway said she was monitoring what her children saw about her online. Trailing the interview, O’Donnell said she asked Conway whether she thought Saturday Night Live, which has lampooned the adviser and her feuds with the press, had gone too far in its depictions of her. The network did not say how Conway answered.